MCR3U1
U4L7
THE SINE LAW
(The Ambiguous Case)
PART A ~ INTRODUCTION
The ambiguous case arises in a SSA (2 sides and an angle opposite one of the sides)
triangle when using the Sine Law. In such a case, the triangle may not be uniquely
determined ~ the Sine Law calculation may lead to 0, 1, or 2 solutions.
PART B ~ INVESTIGATING THE CASES
Example 
In ABC, A = 420, a = 23 cm, and b = 28 cm. Determine B and C to
the nearest a degree.
Case 1 (B is acute)
C
B
A
Case 2 (B is obtuse)
C
A
B
 there are 2 possible solutions
MCR3U1
U4L7
Example 
In ABC, A = 670, a = 10.2 cm, and b = 8.5 cm. Determine B and C to
the nearest a degree.
C
A
B
 there is 1 possible solution
C
A
B
Example 
In ABC, A = 390, a = 10 cm, and b = 25 cm. Determine B and C to
the nearest a degree.
C
A
B
 there is no possible solution
Homework: p.318 #1b, 3bc, 5ac & …
A light in a park can illuminate effectively up to a distance of 100 m.
A point on a bike path is 150 m from the light. The sight line to the
light makes an angle of 230 with the bike path. Determine the length
of the bike path, to the nearest metre, that is effectively illuminated
by the light. [162 m]
?
230
150m
Light